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90 records · Page 5Linked to original sources
USGS1997

Southern California Permanent GPS Geodetic Array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes

The southern California Permanent GPS Geodetic Array (PGGA) was established in 1990 across the Pacific-North America plate boundary to continuously monitor crustal deformation. We describe the development of the array and the time series of daily positions estimated for its first 10 sites in the 19-month period between the June 28, 1992 ( M w =7.3), Landers and January 17, 1994 ( M w =6.7), Northridge earthquakes. We compare displacement rates at four site locations with those reported by Feigl et al. [1993], which were derived from an independent set of Global Positioning System (GPS) and very long baseline interferometry (VLBI) measurements collected over nearly a decade prior to the Landers earthquake. The velocity differences for three sites 65–100 km from the earthquake's epicenter are of order of 3–5 mm/yr and are systematically coupled with the corresponding directions of coseismic displacement. The fourth site, 300 km from the epicenter, shows no significant velocity difference. These observations suggest large-scale postseismic deformation with a relaxation time of at least 800 days. The statistical significance of our observations is complicated by our incomplete knowledge of the noise properties of the two data sets; two possible noise models fit the PGGA data equally well as described in the companion paper by Zhang et al . [this issue]; the pre-Landers data are too sparse and heterogeneous to derive a reliable noise model. Under a fractal white noise model for the PGGA data we find that the velocity differences for all three sites are statistically different at the 99% significance level. A white noise plus flicker noise model results in significance levels of only 94%, 43%, and 88%. Additional investigations of the pre-Landers data, and analysis of longer spans of PGGA data, could have an important effect on the significance of these results and will be addressed in future work.

Journal of Geophysical Research B: Solid Earth↗
USGS2012

Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii

Fractal singularity analysis (FSA) is used to study a 22-year record of deep seismic tremor (30–60 km depth) for regions below Kilauea Volcano on the assumption that magma transport and fracture can be treated as a system of coupled nonlinear oscillators. Tremor episodes range from 1 to 100 min (cumulative duration = 1.60×10 4 min; yearly average = 727 min yr −1 ; mean gradient = 24.2 min yr −1 km −1 ). Partitioning of probabilities, p i , in the phase space of normalized durations, x i , are expressed in terms of a function f(α), where α is a variable exponent of a length scale, ℓ. Plots of f(α) vs. α are called multifractal singularity spectra. The spectrum for deep tremor durations is bounded by α values of about 0.4 and 1.9 at f = 0; f max ≃ 1.0 for α ≃ 1. Results for tremor are similar to those found for systems transitional between complete mode locking and chaos.

Geophysical Research Letters↗
USGS2013

The age of scarplike landforms from diffusion-equation analysis

The purpose of this paper is to review developments in the quantitative modeling of fault-scarp geomorphology, principally those since 1980. These developments utilize diffusionequation mathematics, in several different forms, as the basic model of fault-scarp evolution. Because solutions to the general diffusion equation evolve with time, as we expect faultscarp morphology to evolve with time, the model solutions carry information about the age of the structure and thus its time of formation; hence the inclusion of this paper in this volume. The evolution of fault-scarp morphology holds a small but special place in the much larger class of problems in landform evolution. In general, landform evolution means the evolution of topography as a function of both space and time. It is the outcome of the competition among those tectonic processes that make topography, erosive processes that destroy topography, and depositional processes that redistribute topography. Deposition and erosion can always be coupled through conservation-of-mass relations, but in general deposition occurs at great distance from the source region of detritus. Moreover, erosion is an inherently rough process whereas deposition is inherently smooth, as is evident from even casual inspection of shaded-relief, digital-elevation maps (e.g., Thelin and Pike, 1990; Simpson and Anders, 1992) and the current fascination with fractal representations oferoding terrains (e.g., Huang and Turcotte, 1989; Newman and Turcotte, 1990). Nevertheless, large-scale landform-evolution modeling, now a computationally intensive, advanced numerical exercise, is generating ever more realistic landforms (e.g., Willgoose and others, 1991a,b; Kooi and Beaumont, 1994; Tucker and Slingerland, 1994), although many of the rate coefficients remain poorly prescribed

Book chapter↗
USGS1999

Frequency-magnitude statistics and spatial correlation dimensions of earthquakes at Long Valley caldera, California

Intense earthquake swarms at Long Valley caldera in late 1997 and early 1998 occurred on two contrasting structures. The first is defined by the intersection of a north-northwesterly array of faults with the southern margin of the resurgent dome, and is a zone of hydrothermal upwelling. Seismic activity there was characterized by high b-values and relatively low values of D, the spatial fractal dimension of hypocentres. The second structure is the pre-existing South Moat fault, which has generated large-magnitude seismic activity in the past. Seismicity on this structure was characterized by low b-values and relatively high D. These observations are consistent with low-magnitude, clustered earthquakes on the first structure, and higher-magnitude, diffuse earthquakes on the second structure. The first structure is probably an immature fault zone, fractured on a small scale and lacking a well-developed fault plane. The second zone represents a mature fault with an extensive, coherent fault plane.

Geophysical Journal International↗
USGS2001

Spatial paradigms of lotic diatom distribution: A landscape ecology perspective

Spatial distributional patterns of benthic diatoms and their relation to current velocity were investigated in an unshaded cobble-bottom reach of White Creek (Washington County, NY). On 27 August 1999, diatoms were sampled and current velocity and depth were measured on a regular square sampling grid with a grain size of 0.01 m2, interval of 0.5 m, and extent of 16 m2. The relative abundance of the 18 common diatom species enumerated in the 81 samples was subjected to detrended correspondence analysis (DCA). The first axis (DCA1) explained 51% of the variance in diatom data and separated the samples according to current regimes. The spatial autocorrelation of DCA1 sample scores in deposition and erosion regions of White Creek was determined by Moran's I statistic to indicate patch size. In White Creek the patch length of all diatom communities was more than 3.1 m, whereas the patch width was 1 m in the deposition region and 0.5 m in the erosion region. There were 5 dominant diatom taxa, Achnanthes minutissima Ku??tz. et vars, Fragilaria capucina Dezmazie??res et vars, F. crotonensis Kitt., Diatoma vulgaris Bory, and Synedra ulna (Nitz.) Ehr. et vars. The patch length of the dominant species varied from 1 to more than 4.1 m, whereas the patch width, if defined, was 0.5 m. Achnanthes minutissima and F. capucina, the two diatom species with the highest relative abundance, displayed spatially structured patches of low abundance and comparatively random patches of high abundance, suggesting broad scale abiotic control of species performance in low abundance regions and finer scale biotic control of high abundance areas. Another objective of this study was to test the hypothesis that higher current velocities, which generally impede immigration, would increase randomness and complexity (i.e. homogeneity of diatom distributional patterns). The spatial complexity in low versus high velocity transects was determined by calculating the respective fractal dimension (D) of DCA1 scores. D of DCA1 was higher in the higher current velocity transects, suggesting that spatial complexity and homogeneity of diatom communities increased in faster currents. Partial canonical correspondence analysis was conducted on diatom, environmental, and spatial data to assess how much of the variance in species distribution could be attributed to environmental (current velocity and depth) versus spatial factors. The variance of species data, explained by the environment (exclusively current velocity), was 38%; whereas space alone contributed only 10%, indicating that 1) current velocity was the major factor that controlled diatom distribution in streams and 2) there were other spatially dependent variables, most likely biotic, but their role in shaping diatom communities was minor.

Journal of Phycology↗
USGS2013

Lake shoreline in the contiguous United States: Quantity, distribution and sensitivity to observation resolution

1. Quantifying lake biogeochemical processing at broad spatial scales requires that we scale processes along with physical metrics. Past work has primarily scaled lentic processes using estimates of lake surface area. However, many processes important to lakes, such as material, energy and biological fluxes and biogeochemical cycling, scale with lake perimeter. 2. We estimate the total lake perimeter for the contiguous United States (U.S.) and examine the sensitivity of this estimate to measurement resolution. At the original mapping resolution, lakes in the contiguous U.S. have a total perimeter of over 1.8 million km. 3. The change in measured perimeter versus measurement resolution for the contiguous U.S. had a log-log slope (also known as the fractal dimension) of 0.21, generally less than previously reported estimates. With changing observation resolution, total measured perimeter was most sensitive to the inclusion or exclusion of small lakes, not shoreline complexity. 4. The total aquatic–terrestrial interface in lakes is less than one-tenth that of streams and rivers, which collectively account for over 21 million km of shoreline in the contiguous U.S. This study further describes the distribution of lake perimeter and proposes a technique that can contribute to understanding continental-scale processes.

Freshwater Biology↗
USGS2000

Geomorphometry-Diversity in quantitative surface analysis

A widening variety of applications is diversifying geomorphometry ( digital terrain modelling ), the quantitative study of topography. An amalgam of earth science, mathematics, engineering and computer science, the discipline has been revolutionized by the computer manipulation of gridded terrain heights, or digital elevation models (DEMs). Its rapid expansion continues. This article reviews the remarkable diversity of recent morphometric work in 15 selected topics and discusses their significance and prospects. The quantitative analysis of industrial microsurface topography is introduced to the earth science community. The 14 other topics are Internet access to geomorphometry; global DEMs; DEM modelling of channel networks; self-organized criticality; fractal and wavelet analysis; soil resources; landslide hazards; barchan dunes; harvesting wind energy; sea-ice surfaces; sea-floor abyssal hills; Japanese work in morphometry; and the emerging fields of landscape ecology and image understanding. Closing remarks note reasons for the diversity within geomorphometry, speculate on future trends and recommend creating a unified field of surface representation.

Progress in Physical Geography: Earth and Environm↗
USGS2000

Three-dimensional simulations of ground motions in the Seattle region for earthquakes in the Seattle fault zone

We used the 3D finite-difference method to model observed seismograms of two earthquakes (ML 4.9 and 3.5) in the Seattle region and to simulate ground motions for hypothetical M 6.5 and M 5.0 earthquakes on the Seattle fault, for periods greater than 2 sec. A 3D velocity model of the Seattle Basin was constructed from studies that analyzed seismic-reflection surveys, borehole logs, and gravity and aeromagnetic data. The observations and the simulations highlight the importance of the Seattle Basin on long-period ground motions. For earthquakes occurring just south of the basin, the edge of the basin and the variation of the thickness of the Quaternary deposits in the basin produce much larger surface waves than expected from flat-layered models. The data consist of seismograms recorded by instruments deployed in Seattle by the USGS and the University of Washington (UW). The 3D simulation reproduces the peak amplitude and duration of most of the seismograms of the June 1997 Bremerton event (ML 4.9) recorded in Seattle. We found the focal mechanism for this event that best fits the observed seismograms in Seattle by combining Green's functions determined from the 3D simulations for the six fundamental moment couples. The February 1997 event (ML 3.5) to the south of the Seattle Basin exhibits a large surface-wave arrival at UW whose amplitude is matched by the synthetics in our 3D velocity model, for a source depth of 9 km. The M 6.5 simulations incorporated a fractal slip distribution on the fault plane. These simulations produced the largest ground motions in an area that includes downtown Seattle. This is mainly caused by rupture directed up dip toward downtown, radiation pattern of the source, and the turning of S waves by the velocity gradient in the Seattle basin. Another area of high ground motion is located about 13 km north of the fault and is caused by an increase in the amplitude of higher-mode Rayleigh waves caused by the thinning of the Quaternary deposits.

Bulletin of the Seismological Society of America↗
USGS2002

Simulation of broadband ground motion including nonlinear soil effects for a magnitude 6.5 earthquake on the Seattle fault, Seattle, Washington

The Seattle fault poses a significant seismic hazard to the city of Seattle, Washington. A hybrid, low-frequency, high-frequency method is used to calculate broadband (0-20 Hz) ground-motion time histories for a M 6.5 earthquake on the Seattle fault. Low frequencies (1 Hz) are calculated by a stochastic method that uses a fractal subevent size distribution to give an ω -2 displacement spectrum. Time histories are calculated for a grid of stations and then corrected for the local site response using a classification scheme based on the surficial geology. Average shear-wave velocity profiles are developed for six surficial geologic units: artificial fill, modified land, Esperance sand, Lawton clay, till, and Tertiary sandstone. These profiles together with other soil parameters are used to compare linear, equivalent-linear, and nonlinear predictions of ground motion in the frequency band 0-15 Hz. Linear site-response corrections are found to yield unreasonably large ground motions. Equivalent-linear and nonlinear calculations give peak values similar to the 1994 Northridge, California, earthquake and those predicted by regression relationships. Ground-motion variance is estimated for (1) randomization of the velocity profiles, (2) variation in source parameters, and (3) choice of nonlinear model. Within the limits of the models tested, the results are found to be most sensitive to the nonlinear model and soil parameters, notably the over consolidation ratio.

Washington↗
USGS2005

Calculation of broadband time histories of ground motion, Part II: Kinematic and dynamic modeling using theoretical Green's functions and comparison with the 1994 northridge earthquake

In the evolution of methods for calculating synthetic time histories of ground motion for postulated earthquakes, kinematic source models have dominated to date because of their ease of application. Dynamic models, however, which incorporate a physical relationship between important faulting parameters of stress drop, slip, rupture velocity, and rise time, are becoming more accessible. This article compares a class of kinematic models based on the summation of a fractal distribution of subevent sizes with a dynamic model based on the slip-weakening friction law. Kinematic modeling is done for the frequency band 0.2 to 10.0. Hz, dynamic models are calculated from 0.2 to 2.0. Hz. The strong motion data set for the 1994 Northridge earthquake is used to evaluate and compare the synthetic time histories. Source models are propagated to the far field by convolution with 1D and 3D theoretical Green’s functions. In addition, the kinematic model is used to evaluate the importance of propagation path effects: velocity structure, scattering, and nonlinearity. At present, the kinematic model gives a better broadband fit to the Northridge ground motion than the simple slip-weakening dynamic model. In general, the dynamic model overpredicts rise times and produces insufficient shorter-period energy. Within the context of the slip-weakening model, the Northridge ground motion requires a short slip-weakening distance, on the order of 0.15 m or less. A more complex dynamic model including rate weakening or one that allows shorter rise times near the hypocenter may fit the data better.

Bulletin of the Seismological Society of America↗
USGS2015

Comment on “Models of stochastic, spatially varying stress in the crust compatible with focal‐mechanism data, and how stress inversions can be biased toward the stress rate” by Deborah Elaine Smith and Thomas H. Heaton

Smith and Heaton (2011) propose a model in which stress in the crust is fractal‐like and highly variable on a range of length scales, including short length‐scales of ~1 km. Smith and Heaton (2011) motivate the need for stress heterogeneity on short length‐scales by citing observations such as short length‐scale changes in stress directions inferred from borehole breakouts, short length‐scale changes in earthquake slip, and the success of numerical models that include short‐wavelength stress heterogeneity. The heterogeneous part of the stress field in their model is more than twice as large as the homogeneous part. The stress field in this model frequently reverses itself over short distances, as can be seen in figure14 a of Smith and Heaton (2011). The modeled stress field contains at least 10 areas of reversed shear stress direction over the length of a 100 km long profile, with the length of the reversed areas ranging from <1 to ~5 km. This model makes specific predictions about the orientations and heterogeneity of earthquake focal mechanisms. Smith and Heaton (2011) attempt to validate this heterogeneous stress model using observations of earthquake focal‐mechanism variability from Hardebeck (2006). They then demonstrate that the model predicts a bias in the orientations of earthquake focal mechanisms, which are biased away from the background stress and toward the stressing rate. They suggest the focal‐mechanism bias in this model invalidates the large body of work over the last several decades, that has inferred stress orientations from the inversion of earthquake focal mechanisms. The question of whether or not the Smith and Heaton (2011) model is applicable to the real Earth is therefore important not only for understanding spatial stress variability but also for evaluating the numerous studies that have inferred crustal stress orientations from earthquake focal mechanisms (e.g., as compiled by Heidbach et al. , 2008).

Bulletin of the Seismological Society of America↗
USGS1996

The 1993 Mississippi river flood: A one hundred or a one thousand year event?

Power-law (fractal) extreme-value statistics are applicable to many natural phenomena under a wide variety of circumstances. Data from a hydrologic station in Keokuk, Iowa, shows the great flood of the Mississippi River in 1993 has a recurrence interval on the order of 100 years using power-law statistics applied to partial-duration flood series and on the order of 1,000 years using a log-Pearson type 3 (LP3) distribution applied to annual series. The LP3 analysis is the federally adopted probability distribution for flood-frequency estimation of extreme events. We suggest that power-law statistics are preferable to LP3 analysis. As a further test of the power-law approach we consider paleoflood data from the Colorado River. We compare power-law and LP3 extrapolations of historical data with these paleo-floods. The results are remarkably similar to those obtained for the Mississippi River: Recurrence intervals from power-law statistics applied to Lees Ferry discharge data are generally consistent with inferred 100- and 1,000-year paleofloods, whereas LP3 analysis gives recurrence intervals that are orders of magnitude longer. For both the Keokuk and Lees Ferry gauges, the use of an annual series introduces an artificial curvature in log-log space that leads to an underestimate of severe floods. Power-law statistics are predicting much shorter recurrence intervals than the federally adopted LP3 statistics. We suggest that if power-law behavior is applicable, then the likelihood of severe floods is much higher. More conservative dam designs and land-use restrictions Nay be required.

Environmental & Engineering Geoscience↗
USGS2023

Snow surface roughness across spatio-temporal scales

The snow surface is at the interface between the atmosphere and Earth. The surface of the snowpack changes due to its interaction with precipitation, wind, humidity, short- and long-wave radiation, underlying terrain characteristics, and land cover. These connections create a dynamic snow surface that impacts the energy and mass balance of the snowpack, blowing snow potential, and other snowpack processes. Despite this, the snow surface is generally considered a constant parameter in many Earth system models. Data from the National Aeronautics and Space Administration (NASA) Cold Land Processes Experiment (CLPX) collected in 2002 and 2003 across northern Colorado were used to investigate the spatial and temporal variability of snow surface roughness. The random roughness (RR) and fractal dimension (D) metrics used in this investigation are well correlated. However, roughness is not correlated across scales, computed here from snow roughness boards at a millimeter resolution and airborne lidar at a meter resolution. Process scale differences were found based on land cover at each of the two measurement scales, as appraised through measurements in the forest and alpine.

Colorado↗
USGS1996

Observations of rapid-fire event tremor at Lascar volcano, Chile

During the Proyecto de Investigacio??n Sismolo??gica de la Cordillera Occidental (PISCO '94) in the Atacama desert of Northern Chile, a continuously recording broadband seismic station was installed to the NW of the currently active volcano, Lascar. For the month of April, 1994, an additional network of three, short period, three-component stations was deployed around the volcano to help discriminate its seismic signals from other local seismicity. During the deployment, the volcanic activity at Lascar appeared to be limited mainly to the emission of steam and SO2. Tremor from Lascar is a random, ??rapid-fire?? series of events with a wide range of amplitudes and a quasi-fractal structure. The tremor is generated by an ensemble of independent elementary sources clustered in the volcanic edifice. In the short-term, the excitation of the sources fluctuates strongly, while the long-term power spectrum is very stationary.

Annals of Geophysics↗
USGS2025

The effects of line simplification on planform geometry

Data on maps should retain accuracy regardless of scale. Yet, as cartographic lines are generalized, there can be impacts on properties such as topology, density, and planform geometry. Here, we investigate the use of the Scale Specific Sinuosity (S3) metric (Stanislawski et al., 2023) to evaluate the effects of line simplification on planform geometry, which is the bends of streams in map view. We employ an open-source Python S3 workflow to characterize the geometry of five diverse stream channels in the United States. The original data are extracted from the U.S. Geological Survey National Hydrography Dataset 1:24,000-scale vector data (U.S. Geological Survey, 2000) (Table 1), and the simplification is done using the Visvalingam and Whyatt method (2017) with a simplification tolerance of 0.5, 1.0, 1.5, and 2.0 km. The S3 analysis is calculated at each level of simplification and S3 derivatives are generated. Derivatives include measures of sinuosity, fractal dimension, and the dominant bend wavelength. The findings show that the change in planform geometry is scale-dependent, though simplification will have little effect on straighter lines. The change becomes more apparent in complex lines as the degree of simplification aligns with the scale of the dominant bend geometries. These logical conclusions are evidence that the S3 is a useful metric for automated characterization of bend geometry regardless of line complexity.

Conference Paper↗
USGS1992

Remote sensing studies of the geomorphology of Surtsey, 1987-1991

The volcanic island of Surtsey, formed by explosive submarine and effusive subaerial eruptions between November 1963 and June 1967, consists of a complex combination of primary and redeposited tephra and alkaline olivine basalt lava flows in a 2.5 km 2 area (Thorarinsson, 1967; Thorarinsson et al., 1964; Fridriksson, 1975). During the past 24 years, wave and wind erosion of this subaerial mid-ocean ridge (MOR) vent complex have modified Surtsey's coastal morphology, including the deposition of a 0.5 km-long northern peninsula ( ness ) composed of tephra and rounded lava fragments derived from the southern half of the island. Detailed geomorphologic and sedimentologic mapping of the various surface units now present on Surtsey has been accomplished throughout the history of the evolving island, most recently by Calles et al. (1980) and Ingolfsson (1980). On the basis of these studies, an effort to quantify the topographic characteristics of the primary geomorphic units on the island was initiated by the National Aeronautics and Space Administration (NASA) and the United States Geological Survey (USGS) in 1987. The objective has been to directly measure the microtopographic properties of the widest range of surface types possible, with special emphasis on the pristine or dynamic types. While large-scale topographic maps of Surtsey were prepared in 1968 and 1975 (Norrman, 1980; Norrman and Erlingsson, 1991; Calles et al, 1980), and geodetic leveling surveys have been carried out (Moore, 1980), there have been no recent attempts to geodetically determine the local topography of the island. Because of the rapid rates of geomorphic processes, such as erosion and deposition, on a small, geologically isolated volcanic island such as Surtsey, it is desirable to determine the meter-scale topographic character of its surface units and landforms, and later a remeasurement of the same surfaces to further quantify volumetric change, subsidence, and process rates. In addition, precise measurements of sub-meter-scale topography of pristine geologic surfaces provides necessary data for the investigation of whether various geologic processes demonstrate fractal or self-affine behavior at a range of length-scales within the interval 0.1 in to 1 km. Thus Surtsey offers a unique opportunity to apply new remote sensing techniques to the measurement of the evolving surface "roughness" characteristics of pristine geologic surfaces within an historically well-monitored environment.

Surtsey Research Progress Report↗
USGS2020

Preserving meander bend geometry through scale

Stream meander geometry is a function of hydrologic, geologic, and anthropogenic forces. Meander morphometrics are used in geomorphic classification, ecological characterization, and tectonic and hydrologic change detection. Thus, detailed measurement and classification of meander geometry is imperative to multiscale representation of hydrographic features, which raises important questions. What meander geometries are important to preserve in multi-scale databases? How are geometries measured? How are they preserved? Is the choice between preservation of geometry or use of classification attributes? Questions related to multiscale measurement and representation of hydrographic features continue to emerge with increased spatial and temporal data collection. A key metric for understanding meander bend geometry is sinuosity. The most common measure of sinuosity is the length of a feature divided by the distance between stream head and mouth. The measure relays deviation from a straight line but nothing about meander wavelength. There is not a clear consensus on methods for measuring meander geometry, much less efficiently, at scales made viable with increased data resolution. Here we propose a method for automated characterization of meander wavelength or bend radius. The method, termed Scale-Specific Sinuosity ( S 3 ), is a derivation from the Richardson plot. The Richardson (1961) plot is a classic means of calculating fractal dimension of natural line features and describes feature length (ℓ) given increasing vertex spacing, or step size (S), plotted on a log-log plot. The S 3 metric is defined as negative one times the slope of a Richardson plot for a given stride length. This paper demonstrates utility of S 3 for estimating changes in sinuosity with scale change.

Conference Paper↗
USGS2011

Scaling of flow distance in random self-similar channel networks

Natural river channel networks have been shown in empirical studies to exhibit power-law scaling behavior characteristic of self-similar and self-affine structures. Of particular interest is to describe how the distribution of distance to the outlet changes as a function of network size. In this paper, networks are modeled as random self-similar rooted tree graphs and scaling of distance to the root is studied using methods in stochastic branching theory. In particular, the asymptotic expectation of the width function (number of nodes as a function of distance to the outlet) is derived under conditions on the replacement generators. It is demonstrated further that the branching number describing rate of growth of node distance to the outlet is identical to the length ratio under a Horton-Strahler ordering scheme as order gets large, again under certain restrictions on the generators. These results are discussed in relation to drainage basin allometry and an application to an actual drainage network is presented. ?? World Scientific Publishing Company.

Fractals↗